Problem: Solve for $x$ and $y$ using elimination. ${5x+2y = 50}$ ${6x-2y = 38}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $11x = 88$ $\dfrac{11x}{{11}} = \dfrac{88}{{11}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {5x+2y = 50}\thinspace$ to find $y$ ${5}{(8)}{ + 2y = 50}$ $40+2y = 50$ $40{-40} + 2y = 50{-40}$ $2y = 10$ $\dfrac{2y}{{2}} = \dfrac{10}{{2}}$ ${y = 5}$ You can also plug ${x = 8}$ into $\thinspace {6x-2y = 38}\thinspace$ and get the same answer for $y$ : ${6}{(8)}{ - 2y = 38}$ ${y = 5}$